After rebooting, I get the following notification: VBoxClient: The VirtualBox kernel service is not running. Exiting.

I've googled around and found others having similar issues, but mostly because they'd installed the guest additions on the host, or because there's a mismatch between the guest additions and the kernel version. As far as I can see that's not the case here. I'm adding some details below which I've seen others having asked for: